In an opinion poll before an election, a sample of $30$ voters is obtained. The number of voters in

Question

In an opinion poll before an election, a sample of $30$ voters is obtained. The number of voters in the sample who support the Alliance Party is denoted by $A$. State in context, two conditions that must be assumed for $A$ to be modelled by a Binomial Distribution. It is given that $5\%$ of the voters in the election support the Alliance Party. What is the probability that fewer than $6$ of the $30$ voters support the Alliance Party? [2] What will be the most likely number of voters who support the Alliance Party in a sample of $40$ voters? [2] It is given that, in a sample of $50$ voters, the probability that at least $m$ voters who support the Alliance Party is less than $0.4$. Find the least possible value of $m$. [3] If a sample of $n$ number of voters is obtained and the probability of getting at least a supporter is not more than $0.75$. Find the maximum value of $n$. [3] In the next election, another sample of $30$ voters is obtained and the percentage of the voters is $p$ where $p>50$. It is given that the probability of getting $15$to $20$supporters is $0.3$. Find the value of $p$. [4]

Accepted Answer

(a)(i) $0.997$; (ii) $2$; (iii) least $m=4$; (iv) $27$; (b) $72.4$

N2012 P2 Q9 [Modified]

N2012 P2 Q9 [Modified]

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